Preventing RSS feeds access to the authenticated uses only

Assuming that:

Different types of memberships = different User Roles

You can simply apply some conditional logic to achieve this:

    function disable_rss_conditionally() {
    // First let's check if the user is logged in
    // you can use current_user_can() to pass to forbidden roles    

    if (! is_user_logged_in() || current_user_can( 'subscriber' ) ) {
// you can also use wp_die( __( 'Some message'));
    wp_redirect( home_url(), $status = 404 );
    }
    }


    add_action('do_feed', 'disable_rss_conditionally', 1);
    add_action('do_feed_rdf', 'disable_rss_conditionally', 1);
    add_action('do_feed_rss', 'disable_rss_conditionally', 1);
    add_action('do_feed_rss2', 'disable_rss_conditionally', 1);
    add_action('do_feed_atom', 'disable_rss_conditionally', 1);
    add_action('do_feed_rss2_comments', 'disable_rss_conditionally', 1);
    add_action('do_feed_atom_comments', 'disable_rss_conditionally', 1);